Multi-digit+multiplication

Multi-digit multiplication: More than just the traditional algorithm
Multi-digit multiplication isn't the focus of this course, but doing multi-digit multiplication provides practice for students in their multiplication combinations (even though it is much more complex than just knowing the multiplication facts). Some advice about teaching multi-digit multiplication is included here, as a next step beyond learning the fact families.

You can use this handout to assess students' understanding of multi-digit multiplication: [|Handout 7: Multi-digit multiplication practice problems]. Or use this teacher background paper to analyze students' difficulties with multi-digit multiplication: [|Analyzing computation difficulties]

There are several key concepts that students need to master, in order to be fluent with multi-digit multiplication and multi-digit division. They are explained in detail in this background paper: [|Multiplication and division learning progression].

In short, to get to the point of being able to fluently multiply any two whole numbers, students should


 * 1) Know that the concept of multiplication is repeated adding or skip counting – finding the total number of objects in a set of equal size groups (N.ME.02.04 and N.MR.02.13)
 * 2) Be able to represent situations involving groups of equal size with objects, words and symbols. (N.MR.02.16)
 * 3) Know multiplication combinations fluently (which may mean some flexible use of derived strategies).
 * 4) Know how to multiply by 10 and 100. (N.FL.03.13)
 * 5) Use number sense to estimate the result of multiplying.
 * 6) Use arrays and [|area models] to represent multiplication (N.MR.02.14) and to simplify calculations.
 * 7) Understand how the distributive property works and use it to simplify calculations. (N.ME.04.09 Multiply two-digit numbers by 2, 3, 4, and 5, using the distributive property…) For example: 46 x 5 = (40 x 5) + (6 x 5) = 200 + 30.
 * 8) Use alternative algorithms like the [|partial product method] (based on the distributive property) and the [|lattice method].
 * 9) Identify typical errors that occur when using the standard algorithm. (N.FL.05.04) For example, see if you can figure out this: [[image:typical_error2.jpg]]